arXiv subjects

Josef Grus

Publications and source records attributed to Josef Grus.

6 recordsLinked to original sources

arXiv2026

Periodic Scheduling of Grouped Time-Triggered Signals on a Single Resource

Time-triggered messages are of crucial importance in modern communication networks. Offline-generated schedules, which specify start times for periodic messages, enable us to achieve deterministic behavior in critical applications. In automotive and avionics domains, so-called signals (measurements and commands) are periodically generated and communicated (via messages) among sensors, controllers, and actuators. However, the message contains not only the useful signal data, but also necessary metadata, e.g., message ID. Metadata is stored as a header or tail and extends the message size; when the signal is very short (as it often is in applications), sending each in a separate message is inefficient. Thus, several signals are grouped into a single message, depending on their periodicity and length, and sent with just one header. Such an approach increases the utilization of the communication resource (link or bus), since less bandwidth is wasted on headers (Kuaban et al. 2021). However, grouping the signals into messages is complicated. The maximum size of the message (including the metadata) is finite, since longer messages have a lower probability of successful delivery. Also, longer messages are less flexible for scheduling in a periodic setting. This is similar to the work of Huan et al. (2019), where the compromise between energy efficiency and latency for IoT devices was investigated. In this paper, we study the fundamental problem of grouping time-triggered signals into messages and periodic scheduling of messages on a single resource.

cs.NI↗

arXiv2025

Hierarchical Rectangle Packing Solved by Multi-Level Recursive Logic-based Benders Decomposition

We study the two-dimensional hierarchical rectangle packing problem, motivated by applications in analog integrated circuit layout, facility layout, and logistics. Unlike classical strip or bin packing, the dimensions of the container are not fixed, and the packing is inherently hierarchical: each item is either a rectangle or a block occurrence, whose dimensions are a solution of another packing problem. This recursive structure reflects real-world scenarios in which components, boxes, or modules must be packed within higher-level containers. We formally define the problem and propose exact formulations in Mixed-Integer Linear Programming and Constraint Programming. Given the computational difficulty of solving complex packing instances directly, we propose decomposition heuristics. First, we implement an existing Bottom-Up baseline method that solves subblocks before combining them at higher levels. Building upon this, we introduce a novel multilevel Logic-based Benders Decomposition method. This heuristic method dynamically refines block dimension constraints, eliminating the need for manual selection of candidate widths or aspect ratios. Experiments on synthetic instances with up to seven hierarchy levels, 80 items per block, and limited computation time show that the proposed decomposition significantly outperforms both monolithic formulations and the Bottom-Up method in terms of solution quality and scalability.

cs.CG↗

arXiv2025

Periodic Chains Scheduling on Dedicated Resources -- A Crucial Problem in Time-Sensitive Networks

Periodic messages transfer data from sensors to actuators in cars, planes, and complex production machines. When considering a given routing, the unicast message starts at its source and goes over several dedicated resources to reach its destination. Such unicast message can be represented as a chain of point-to-point communications. Thus, the scheduling of the periodic chains is a principal problem in time-triggered Ethernet, like IEEE 802.1Qbv Time-Sensitive Networks. This paper studies a strongly NP-hard periodic scheduling problem with harmonic periods, task chains, and dedicated resources. We analyze the problem on several levels of generality and complexity and provide the corresponding proofs. We describe a solution methodology to find a feasible schedule that minimizes the chains' degeneracy related to start-to-end latency normalized in the number of periods. We use the local search with the first fit scheduling heuristic, which we warm-start with a constraint programming model. This notably improves the schedulability of instances with up to 100% utilization and thousands (and more) of tasks, with high-quality solutions found in minutes. An efficient constraint programming matheuristic significantly reduces the degeneracy of the found schedules even further. The method is evaluated on sets of industrial-, avionic-, and automotive-inspired instances.

cs.NI↗

arXiv2024

Matheuristic Local Search for the Placement of Analog Integrated Circuits

The suboptimal physical design of the integrated circuits may not only increase the manufacturing costs due to the larger size of the chip but can also impact its performance by placing interconnected rectangular devices too far from each other. In the domain of Analog and Mixed-Signal Integrated Circuits (AMS ICs), placement automation is lacking behind its digital counterpart, mainly due to the variety of components and complex constraints the placement needs to satisfy. Integer Linear Programming (ILP) is a suitable approach to modeling the placement problem for AMS ICs. However, not even state-of-the-art solvers can create high-quality placements for large problem instances. In this paper, we study how to improve the results of our previous ILP model, first by introducing additional constraints and second by using matheuristics. Given the initial solution we obtain using our original ILP model, we use the solver to perform a local search. We try to improve the criterion by considering only a few spatially close rectangles while keeping the rest of the placement fixed. This local search approach enables us to significantly improve the quality of instances whose solution space we could not sufficiently explore before, even when the computation time reserved for the matheuristic is limited. Finally, we evaluate our revised approach on synthetically generated instances containing more than 200 independent rectangles and on real-life problems.

cs.OH↗

arXiv2024

Automated Placement of Analog Integrated Circuits using Priority-based Constructive Heuristic

This paper presents a heuristic approach for solving the placement of Analog and Mixed-Signal Integrated Circuits. Placement is a crucial step in the physical design of integrated circuits. During this step, designers choose the position and variant of each circuit device. We focus on the specific class of analog placement, which requires so-called pockets, their possible merging, and parametrizable minimum distances between devices, which are features mostly omitted in recent research and literature. We formulate the problem using Integer Linear Programming and propose a priority-based constructive heuristic inspired by algorithms for the Facility Layout Problem. Our solution minimizes the perimeter of the circuit's bounding box and the approximated wire length. Multiple variants of the devices with different dimensions are considered. Furthermore, we model constraints crucial for the placement problem, such as symmetry groups and blockage areas. Our outlined improvements make the heuristic suitable to handle complex rules of placement. With a search guided either by a Genetic Algorithm or a Covariance Matrix Adaptation Evolution Strategy, we show the quality of the proposed method on both synthetically generated and real-life industrial instances accompanied by manually created designs. Furthermore, we apply reinforcement learning to control the hyper-parameters of the genetic algorithm. Synthetic instances with more than 200 devices demonstrate that our method can tackle problems more complex than typical industry examples. We also compare our method with results achieved by contemporary state-of-the-art methods on the MCNC and GSRC datasets.

cs.NE↗

arXiv2024

Packing-Inspired Algorithms for Periodic Scheduling Problems with Harmonic Periods

We tackle the problem of non-preemptive periodic scheduling with a harmonic set of periods. Problems of this kind arise within domains of periodic manufacturing and maintenance, and also during the design of industrial, automotive, and avionics communication protocols, where efficient scheduling of messages is crucial for the performance of a time-triggered network. We consider the decision variant of the periodic scheduling problem on a single highly-utilized machine. We first prove a bijection between periodic scheduling and a particular (so-called height-divisible) 2D packing of rectangles. We formulate the problem using Constraint Programming and compare it with equivalent state-of-the-art Integer Linear Programming formulation, showing the former's superiority on difficult instances. Furthermore, we develop a packing-inspired first fit heuristic, which we compare with methods described in the literature. We justify our proposed methods on synthetically generated problem instances inspired by the communication of messages on one channel.

cs.DS↗